The problem of lossless data compression with side information available to both the encoder and the decoder is considered. The finite-blocklength fundamental limits of the best achievable performance are defined, in two different versions of the problem: Reference-based compression , when a single side information string is used repeatedly in compressing different source messages, and pair-based compression , where a different side information string is used for each source message. General achievability and converse theorems are established for arbitrary source-side information pairs. Nonasymptotic normal approximation expansions are proved for the optimal rate in both the reference-based and pair-based settings, for memoryless sources. These are stated in terms of explicit, finite-blocklength bounds, that are tight up to third-order terms. Extensions that go significantly beyond the class of memoryless sources are obtained. The relevant source dispersion is identified and its relationship with the conditional varentropy rate is established. Interestingly, the dispersion is different in reference-based and pair-based compression, and it is proved that the reference-based dispersion is in general smaller.

中文翻译：

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具有辅助信息的无损数据压缩的基本限制

考虑了具有可用于编码器和解码器的辅助信息的无损数据压缩的问题。在两种不同版本的问题中，定义了可达到的最佳性能的有限块长基本限制：基于参考的压缩 ，当重复使用单个辅助信息字符串压缩不同的源消息时，以及 基于对的压缩 ，其中每个源消息使用不同的辅助信息字符串。针对任意源端信息对建立了一般可实现性和逆定理。对于无记忆源，在基于参考值和基于对的设置中，非渐近正态逼近展开被证明具有最佳速率。这些以明确的，有限的块长范围来表示，严格限制为三阶项。获得了远远超出无记忆源类别的扩展。确定相关的源色散，并建立其与条件变率的关系。有趣的是，色散在基于参考的压缩和基于对的压缩中有所不同，并且证明了基于参考的色散通常较小。